Electrostatics in the presence of dielectrics: The benefits of treating the induced surface charge density directly

American Journal of Physics

Volumn 72, Issue 2, 2004, Pages 190-196

  Doerr, T P ^a   Yu, Yi Kuo ^a,b  

^a NATIONAL INSTITUTES OF HEALTH   (United States)

^b FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1042291397     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1624115     Document Type: Article

References (18)

1. Yi-Kuo Yu, "On a class of integrals of Legendre polynomials with complicated arguments-with applications in electrostatics and biomolecular modeling," Physica A 326, 522-533 (2003).
2. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
3. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
4. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
5. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
6. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
7. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
8. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
9. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
10. The following is a selection of textbooks that discuss electrostatics, but do not mention the surface charge method. D. J. Griffiths, Introduction to Electrodynamics (Prentice Hall, Englewood Cliffs, NJ, 1981); J. D. Jackson, Classical Electrodynamics, 2nd ed. (Wiley, New York, 1975); P. Lorrain, D. R. Corson, and F. Lorrain, Electromagnetic Fields and Waves, 3rd ed. (W. H. Freeman, New York, 1988); G. L. Pollack and D. R. Stump, Electromagnetism (Addison Wesley, San Francisco, 2002); M. Schwartz, Principles of Electrodynamics (Dover, New York, 1987); O. D. Jefimenko, Electricity and Magnetism, 2nd ed. (Electret Scientific Co., Star City, WV, 1989); J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941); W. K. H. Panofsky and M. Phillips, Classical Electricity and Magnetism (Addison-Wesley, Reading, MA, 1955); L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 2nd ed. (Pergamon, New York, 1984).
11. T. Sometani and K. Hasebe, "Method for solving electrostatic problems having a simple dielectric boundary," Am. J. Phys. 45, 918-921 (1977).
12. Rosalind Allen, Jean-Pierre Hansen, and Simone Melchionna, "Electrostatic potential inside ionic solutions confined by dielectrics: a variational approach," Phys. Chem. Chem. Phys. 3, 4177-4186 (2001).
13. f/ε.
14. ex which must be the total charge of the charge distribution.
15. If we let either dielectric constant go to infinity, we recover the case of a conductor. If the other dielectric constant is set to unity, corresponding to vacuum, we recover a situation commonly discussed in textbooks. See, for example, Griffiths, Ref. 2, pp. 85-93.
16. lndeed, the dielectric constants of the various finite pieces of material need not all be the same, but in order to avoid excessively elaborate notation at this stage, attention will be restricted to the case indicated. The generalization is straightforward.
17. See nearly any of the books in Ref. 2. Griffiths contains a notably lucid explanation.
18. 2 = π/2.